When the problem says "Angel transformed the following equation from 6x+4-×=2 (×+1) to
10=2 (×+1). He then stated that the solution to the equation is ×=4. Is he correct? Explain"
when I solved the equation I got 24=10 and 10=10. However, im having trouble explaining it... please help!
6 x + 4 - x = 2(x+1) ???
5 x + 4 = 2 x + 2
3 x = -2
x = -2/3
To address this problem and determine if Angel's solution is correct, let's work through step-by-step.
Starting with the equation provided:
6x + 4 - × = 2 (× + 1)
Angel claims to have transformed the equation to:
10 = 2 (× + 1)
Now, to check if Angel's solution is correct, we need to substitute the value × = 4 back into both equations and see if they are indeed true.
For the original equation:
6x + 4 - × = 2 (× + 1)
Substituting × = 4:
6(4) + 4 - 4 = 2(4 + 1)
Which simplifies to:
24 + 4 - 4 = 2(5)
28 = 10
So, when we substitute × = 4 into the original equation, we get 28 = 10, not 10 = 10 or any equation that agrees with what Angel has stated.
Therefore, Angel's solution is incorrect. The correct solution must satisfy the equation, and in this case, × = 4 does not work.
It seems you made a mistake in your explanation because you stated that you obtained 24 = 10 and 10 = 10. Instead, it should be 28 = 10, which contradicts Angel's claim.